Considering time as flowing (A-theorists) i.e., not the Einsteinian block universe (B-theorists; tenseless), although the causality logic is actually the same.
Continuity of causality can instead be thought of as simply counting the number of physical changes that occur in the universe, regardless of whether a given change is localised within some piece of matter, or a spontaneous emergence of particles.
A supposed infinite count of physical changes having occurred previously, would mean a break in the sequential number of events that must have occurred to arrive at now; a break in the spacetime continuum.
Example: Some event which is supposed to have happened infinitely long ago, cannot have a time/date reference relative to our present-day existence, because if it did, it would simply be at some finite point in the past. Therefore, any causal effect which could theoretically continue to our present day would have to progress (count) an infinite number of days, and because it's not possible to count to infinity, this reveals a paradox – a break in the chain of causality.
This is a contradiction, and time being stopped via any means, including a theoretical singularity, does not escape the contradiction if a sequence of events led to the singularity.
Just this very basic analysis proves that time (causality) cannot be infinite in the past.
Distinction between past and future – Presented by: Chico the Philosurfer.
A great article: “Why Past History Cannot Be Infinite: There Must Be a Beginning” – Kirk Durston – link to: “Infinity Articles & Websites”